Five Texture Zeros for Dirac Neutrino Mass Matrices

In this work, we propose new five texture zeros for the mass matrices in the lepton sector in order to predict neutrino masses. In our approach, we extend beyond the Standard Model by assuming Dirac masses for the neutrinos, a feature which allows us to make a theoretical prediction for the lightest neutrino mass in the normal ordering. The textures that were analyzed have enough free parameters to adjust the $V_{\text{\tiny PMNS}}$ mixing matrix including the CP-violating phase, the neutrino mass squared differences $\delta m_{21}^2, \delta m_{31}^2$, and the three charged lepton masses. In order to obtain reliable results, we used two different procedures that are based on the weak basis transformation, a well known technique to analyze textures and their implications for flavor physics. The first method was based on a least-squares analysis to theoretically fit the lepton masses and the mixing parameters to their corresponding experimental values; for this case, the best fit obtained for the lightest neutrino mass was $(3.9\pm^{0.6}_{0.8})\times 10^{-3}$~eV. The second approach was algebraic, resulting in a lightest neutrino mass consistent with the experimental values and the restrictions arising from the five texture zeros of the mass matrices, and the lightest neutrino mass obtained was $(3.5\pm0.9)\times 10^{-3}$~eV